%------------------------------------------------------------------------------
% File     : Metis---2.4
% Problem  : SET024-7 : TPTP v8.1.0. Bugfixed v2.1.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : metis --show proof --show saturation %s

% Computer : n017.cluster.edu
% Model    : x86_64 x86_64
% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory   : 8042.1875MB
% OS       : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit  : 600s
% DateTime : Tue Jul 19 03:31:25 EDT 2022

% Result   : Unsatisfiable 6.80s 7.02s
% Output   : CNFRefutation 6.80s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    5
%            Number of leaves      :    5
% Syntax   : Number of clauses     :   12 (   8 unt;   0 nHn;   8 RR)
%            Number of literals    :   17 (   3 equ;   6 neg)
%            Maximal clause size   :    3 (   1 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of predicates  :    4 (   1 usr;   1 prp; 0-2 aty)
%            Number of functors    :    4 (   4 usr;   2 con; 0-2 aty)
%            Number of variables   :    5 (   3 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(unordered_pair2,axiom,
    ( ~ member(X,universal_class)
    | member(X,unordered_pair(X,Y)) ) ).

cnf(singleton_set,axiom,
    unordered_pair(X,X) = singleton(X) ).

cnf(prove_set_in_its_singleton_1,negated_conjecture,
    member(x,universal_class) ).

cnf(prove_set_in_its_singleton_2,negated_conjecture,
    ~ member(x,singleton(x)) ).

cnf(refute_0_0,plain,
    ( ~ member(x,universal_class)
    | member(x,unordered_pair(x,X_314)) ),
    inference(subst,[],[unordered_pair2:[bind(X,$fot(x)),bind(Y,$fot(X_314))]]) ).

cnf(refute_0_1,plain,
    member(x,unordered_pair(x,X_314)),
    inference(resolve,[$cnf( member(x,universal_class) )],[prove_set_in_its_singleton_1,refute_0_0]) ).

cnf(refute_0_2,plain,
    member(x,unordered_pair(x,x)),
    inference(subst,[],[refute_0_1:[bind(X_314,$fot(x))]]) ).

cnf(refute_0_3,plain,
    unordered_pair(x,x) = singleton(x),
    inference(subst,[],[singleton_set:[bind(X,$fot(x))]]) ).

cnf(refute_0_4,plain,
    ( unordered_pair(x,x) != singleton(x)
    | ~ member(x,unordered_pair(x,x))
    | member(x,singleton(x)) ),
    introduced(tautology,[equality,[$cnf( member(x,unordered_pair(x,x)) ),[1],$fot(singleton(x))]]) ).

cnf(refute_0_5,plain,
    ( ~ member(x,unordered_pair(x,x))
    | member(x,singleton(x)) ),
    inference(resolve,[$cnf( $equal(unordered_pair(x,x),singleton(x)) )],[refute_0_3,refute_0_4]) ).

cnf(refute_0_6,plain,
    member(x,singleton(x)),
    inference(resolve,[$cnf( member(x,unordered_pair(x,x)) )],[refute_0_2,refute_0_5]) ).

cnf(refute_0_7,plain,
    $false,
    inference(resolve,[$cnf( member(x,singleton(x)) )],[refute_0_6,prove_set_in_its_singleton_2]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.13  % Problem  : SET024-7 : TPTP v8.1.0. Bugfixed v2.1.0.
% 0.03/0.13  % Command  : metis --show proof --show saturation %s
% 0.13/0.35  % Computer : n017.cluster.edu
% 0.13/0.35  % Model    : x86_64 x86_64
% 0.13/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35  % Memory   : 8042.1875MB
% 0.13/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35  % CPULimit : 300
% 0.13/0.35  % WCLimit  : 600
% 0.13/0.35  % DateTime : Sun Jul 10 07:28:02 EDT 2022
% 0.13/0.35  % CPUTime  : 
% 0.13/0.35  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 6.80/7.02  % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 6.80/7.02  
% 6.80/7.02  % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 6.80/7.02  
%------------------------------------------------------------------------------